Finite Group Databasebeta

← C17×#3345 #14526351

Subgroups — C17×#3345 #14526351

Order 2176.

388 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C17×#553C211yesmaximal, characteristic, complemented
2C17×#547C211yesmaximal, characteristic, complemented
3C17×#501C211yesmaximal, characteristic, complemented
4C17×#482C211yesmaximal, characteristic, complemented
5C17×#481C211yesmaximal, characteristic, complemented
6C17×#481C211yesmaximal, characteristic, complemented
7C17×#480C211yesmaximal, characteristic, complemented
8C17×#478C211yesmaximal, characteristic, complemented
9C17×#476C211yesmaximal, characteristic, complemented
10C17×#469C211yesmaximal, characteristic, complemented
11C17×#466C211yesmaximal, characteristic, complemented
12C17×#442C211yesmaximal, characteristic, complemented
13C17×#435C211yesmaximal, characteristic, complemented
14C17×#428C211yesmaximal, characteristic, complemented
15C2×C17×#106C211yesmaximal, characteristic, complemented
16C2×#41×C17—21no—
17C2×D8×C17C2211yescharacteristic
18C2×M16×C17C2211yescharacteristic
19C22×C8×C17C2211yescharacteristic
20C17×C4⋊Q8C2211yescharacteristic
21C17×#126—21no—
22C17×#125C2211yescharacteristic
23C17×#123—21no—
24C17×#123—21no—
25C17×#123—21no—
26C17×C22⋊Q8—21no—
27C17×#121—21no—
28C17×#121C2211yescharacteristic
29C17×#121C2211yescharacteristic
30C17×#121C2211yescharacteristic
31C17×#121C2211yescharacteristic
32C4×D4×C17—21no—
33C4×D4×C17C2211yescharacteristic
34C4×D4×C17C2211yescharacteristic
35C4×D4×C17C2211yescharacteristic
36C17×#117C2211yescharacteristic
37C2×C4⋊C4×C17C2211yescharacteristic
38C2×C4⋊C4×C17C2211yescharacteristic
39C2×C4⋊C4×C17C2211yescharacteristic
40C17×#107C2211yescharacteristic
41C17×#107C2211yescharacteristic
42C17×#107C2211yescharacteristic
43C17×#106C2211yescharacteristic
44C17×#106C2211yescharacteristic
45C17×#106C2211yescharacteristic
46C17×#106C2211yescharacteristic
47C17×#106C2211yescharacteristic
48C17×#106C2211yescharacteristic
49C17×C4⋊C8C2211yescharacteristic
50C17×#102C2211yescharacteristic
51C17×#102C2211yescharacteristic
52C17×#102C2211yescharacteristic
53C17×#102C2211yescharacteristic
54C17×#102C2211yescharacteristic
55C17×#102C2211yescharacteristic
56C17×C22⋊C8C2211yescharacteristic
57C17×C22⋊C8C2211yescharacteristic
58C17×#97C2211yescharacteristic
59#41×C17—44no—
60C2×Q8×C17—21no—
61C2×D4×C17—21no—
62C2×D4×C17—21no—
63C2×D4×C17—21no—
64C2×D4×C17—21no—
65C2×D4×C17D411yescharacteristic
66C2×D4×C17C2311yescharacteristic
67C2×D4×C17C2311yescharacteristic
68C22×C4×C17—21no—
69C22×C4×C17—21no—
70C22×C4×C17—21no—
71C22×C4×C17—21no—
72C22×C4×C17—21no—
73C22×C4×C17C2311yescharacteristic
74C22×C4×C17C2311yescharacteristic
75D8×C17—22no—
76M16×C17—22no—
77C2×C8×C17—22no—
78C2×C8×C17C2311yescharacteristic
79C2×C8×C17C2311yescharacteristic
80C2×C8×C17C2311yescharacteristic
81C2×C8×C17C2311yescharacteristic
82C4⋊C4×C17—21no—
83C4⋊C4×C17—21no—
84C4⋊C4×C17—21no—
85C4⋊C4×C17—21no—
86C4⋊C4×C17—21no—
87C4⋊C4×C17—21no—
88C4⋊C4×C17D411yescharacteristic
89C4⋊C4×C17C2311yescharacteristic
90C4⋊C4×C17C2311yescharacteristic
91C4⋊C4×C17C2311yescharacteristic
92C4⋊C4×C17C2311yescharacteristic
93C4⋊C4×C17C2311yescharacteristic
94C4⋊C4×C17C2311yescharacteristic
95C22⋊C4×C17—21no—
96C22⋊C4×C17—21no—
97C22⋊C4×C17—21no—
98C22⋊C4×C17—21no—
99C22⋊C4×C17—21no—
100C22⋊C4×C17—21no—
101C22⋊C4×C17—21no—
102C22⋊C4×C17D411yescharacteristic
103C22⋊C4×C17D411yescharacteristic
104C42×C17—21no—
105C42×C17C2311yescharacteristic
106C23×C17—21no—
107C23×C17—21no—
108C23×C17C2×D411yescharacteristic
109C23×C17C2×D411yescharacteristic
110Q8×C17—42no—
111D4×C17—22no—
112D4×C17—21no—
113D4×C17—21no—
114D4×C17—21no—
115D4×C17—21no—
116D4×C17—42no—
117D4×C17—42no—
118D4×C17—42no—
119D4×C17—81no—
120C2×C4×C17—21no—
121C2×C4×C17—21no—
122C2×C4×C17—21no—
123C2×C4×C17—21no—
124C2×C4×C17—21no—
125C2×C4×C17—21no—
126C2×C4×C17—21no—
127C2×C4×C17—21no—
128C2×C4×C17—21no—
129C2×C4×C17—21no—
130C2×C4×C17—42no—
131C2×C4×C17—42no—
132C2×C4×C17—42no—
133C2×C4×C17—81no—
134C2×C4×C17—81no—
135C2×C4×C17C2×D411yescharacteristic
136C2×C4×C17C2×D411yescharacteristic
137C2×C4×C17C2×D411yescharacteristic
138C2×C4×C17C2×D411yescharacteristic
139C2×C4×C17C2411yescharacteristic
140C8×C17—21no—
141C8×C17—21no—
142C8×C17—21no—
143C8×C17#4112yescomplemented
144#3345C1711yesmaximal, characteristic, direct product factor, Sylow
145C22×C17—21no—
146C22×C17—21no—
147C22×C17—21no—
148C22×C17—21no—
149C22×C17—21no—
150C22×C17—41no—
151C22×C17—41no—
152C22×C17—41no—
153C22×C17—41no—
154C22×C17—41no—
155C22×C17—41no—
156C22×C17AGL(1,ℤ/8)12yes—
157C22×C17C22×D411yescharacteristic
158C4×C17—21no—
159C4×C17—21no—
160C4×C17—21no—
161C4×C17—21no—
162C4×C17—41no—
163C4×C17—41no—
164C4×C17—41no—
165C4×C17—41no—
166C4×C17—41no—
167C4×C17—41no—
168C4×C17C2×#4111yescharacteristic
169C4×C172−1+411yescharacteristic
170#553C2×C1711yescharacteristic, complemented
171#547C2×C1711yescharacteristic, complemented
172#501C2×C1711yescharacteristic, complemented
173#482C2×C1711yescharacteristic, complemented
174#481C2×C1711yescharacteristic, complemented
175#481C2×C1711yescharacteristic, complemented
176#480C2×C1711yescharacteristic, complemented
177#478C2×C1711yescharacteristic, complemented
178#476C2×C1711yescharacteristic, complemented
179#469C2×C1711yescharacteristic, complemented
180#466C2×C1711yescharacteristic, complemented
181#442C2×C1711yescharacteristic, complemented
182#435C2×C1711yescharacteristic, complemented
183#428C2×C1711yescharacteristic, complemented
184C2×#106C2×C1711yescharacteristic, complemented
185C2×C17—22no—
186C2×C17—41no—
187C2×C17—81no—
188C2×C17—81no—
189C2×C17#54711yescharacteristic
190C2×C17C2×AGL(1,ℤ/8)11yescharacteristic
191C2×C17#57711yescharacteristic
192C2×#41—21no—
193C2×D8C22×C1711yescharacteristic
194C2×M16C22×C1711yescharacteristic
195C22×C8C22×C1711yescharacteristic
196C4⋊Q8C22×C1711yescharacteristic
197#126—21no—
198#125C22×C1711yescharacteristic
199#123—21no—
200#123—21no—
201#123—21no—
202C22⋊Q8—21no—
203#121—21no—
204#121C22×C1711yescharacteristic
205#121C22×C1711yescharacteristic
206#121C22×C1711yescharacteristic
207#121C22×C1711yescharacteristic
208C4×D4—21no—
209C4×D4C22×C1711yescharacteristic
210C4×D4C22×C1711yescharacteristic
211C4×D4C22×C1711yescharacteristic
212#117C22×C1711yescharacteristic
213C2×C4⋊C4C22×C1711yescharacteristic
214C2×C4⋊C4C22×C1711yescharacteristic
215C2×C4⋊C4C22×C1711yescharacteristic
216#107C22×C1711yescharacteristic
217#107C22×C1711yescharacteristic
218#107C22×C1711yescharacteristic
219#106C22×C1711yescharacteristic
220#106C22×C1711yescharacteristic
221#106C22×C1711yescharacteristic
222#106C22×C1711yescharacteristic
223#106C22×C1711yescharacteristic
224#106C22×C1711yescharacteristic
225C4⋊C8C22×C1711yescharacteristic
226#102C22×C1711yescharacteristic
227#102C22×C1711yescharacteristic
228#102C22×C1711yescharacteristic
229#102C22×C1711yescharacteristic
230#102C22×C1711yescharacteristic
231#102C22×C1711yescharacteristic
232C22⋊C8C22×C1711yescharacteristic
233C22⋊C8C22×C1711yescharacteristic
234#97C22×C1711yescharacteristic
235C17#334511yescharacteristic, direct product factor, Sylow
236#41—44no—
237C2×Q8—21no—
238C2×D4—21no—
239C2×D4—21no—
240C2×D4—21no—
241C2×D4—21no—
242C2×D4D4×C1711yescharacteristic
243C2×D4C23×C1711yescharacteristic
244C2×D4C23×C1711yescharacteristic
245C22×C4—21no—
246C22×C4—21no—
247C22×C4—21no—
248C22×C4—21no—
249C22×C4—21no—
250C22×C4C23×C1711yescharacteristic
251C22×C4C23×C1711yescharacteristic
252D8—22no—
253M16—22no—
254C2×C8—22no—
255C2×C8C23×C1711yescharacteristic
256C2×C8C23×C1711yescharacteristic
257C2×C8C23×C1711yescharacteristic
258C2×C8C23×C1711yescharacteristic
259C4⋊C4—21no—
260C4⋊C4—21no—
261C4⋊C4—21no—
262C4⋊C4—21no—
263C4⋊C4—21no—
264C4⋊C4—21no—
265C4⋊C4D4×C1711yescharacteristic
266C4⋊C4C23×C1711yescharacteristic
267C4⋊C4C23×C1711yescharacteristic
268C4⋊C4C23×C1711yescharacteristic
269C4⋊C4C23×C1711yescharacteristic
270C4⋊C4C23×C1711yescharacteristic
271C4⋊C4C23×C1711yescharacteristic
272C22⋊C4—21no—
273C22⋊C4—21no—
274C22⋊C4—21no—
275C22⋊C4—21no—
276C22⋊C4—21no—
277C22⋊C4—21no—
278C22⋊C4—21no—
279C22⋊C4D4×C1711yescharacteristic
280C22⋊C4D4×C1711yescharacteristic
281C42—21no—
282C42C23×C1711yescharacteristic
283C23—21no—
284C23—21no—
285C23C2×D4×C1711yescharacteristic
286C23C2×D4×C1711yescharacteristic
287Q8—42no—
288D4—22no—
289D4—21no—
290D4—21no—
291D4—21no—
292D4—21no—
293D4—42no—
294D4—42no—
295D4—42no—
296D4—81no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—42no—
308C2×C4—42no—
309C2×C4—42no—
310C2×C4—81no—
311C2×C4—81no—
312C2×C4C2×D4×C1711yescharacteristic
313C2×C4C2×D4×C1711yescharacteristic
314C2×C4C2×D4×C1711yescharacteristic
315C2×C4C2×D4×C1711yescharacteristic
316C2×C4C24×C1711yescharacteristic
317C8—21no—
318C8—21no—
319C8—21no—
320C8#41×C1712yescomplemented
321C22—21no—
322C22—21no—
323C22—21no—
324C22—21no—
325C22—21no—
326C22—41no—
327C22—41no—
328C22—41no—
329C22—41no—
330C22—41no—
331C22—41no—
332C22C17×AGL(1,ℤ/8)12yes—
333C22C22×D4×C1711yescharacteristic
334C4—21no—
335C4—21no—
336C4—21no—
337C4—21no—
338C4—41no—
339C4—41no—
340C4—41no—
341C4—41no—
342C4—41no—
343C4—41no—
344C4C2×#41×C1711yescharacteristic
345C4C17×2−1+411yescharacteristic
346C2—22no—
347C2—41no—
348C2—81no—
349C2—81no—
350C2C17×#54711yescharacteristic
351C2C2×C17×AGL(1,ℤ/8)11yescharacteristic
352C2C17×#57711yescharacteristic
subgroupG/H
center, socleC22×C17C22×D4
commutator, Frattini, cosocleC2×C4C24×C17
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C17 ◁ C4×D4×C17 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C17×#553C2semidirect
2. C17×#547C2semidirect
3. C17×#501C2semidirect
4. C17×#482C2semidirect
5. C17×#481C2semidirect
6. C17×#481C2semidirect
7. C17×#480C2semidirect
8. C17×#478C2semidirect
9. C17×#476C2semidirect
10. C17×#469C2semidirect
11. C17×#466C2semidirect
12. C17×#442C2semidirect
13. C17×#435C2semidirect
14. C17×#428C2semidirect
15. C2×C17×#106C2semidirect
143. C8×C17#41semidirect
144. #3345C17direct (N × H)
170. #553C2×C17semidirect
171. #547C2×C17semidirect
172. #501C2×C17semidirect
173. #482C2×C17semidirect
174. #481C2×C17semidirect
175. #481C2×C17semidirect
176. #480C2×C17semidirect
177. #478C2×C17semidirect
178. #476C2×C17semidirect
179. #469C2×C17semidirect
180. #466C2×C17semidirect
181. #442C2×C17semidirect
182. #435C2×C17semidirect
183. #428C2×C17semidirect
184. C2×#106C2×C17semidirect
235. C17#3345direct (N × H)
320. C8#41×C17semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C17×#5532
C17×#5472
C17×#5012
C17×#4822
C17×#4812
C17×#4802
C17×#4782
C17×#4762
C17×#4692
C17×#4662
C17×#4422
C17×#4352
C17×#4282
C2×C17×#1062
#334517